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A multilevel method with correction by aggregation for solving discrete elliptic problems

Radim Blaheta (1986)

Aplikace matematiky

The author studies the behaviour of a multi-level method that combines the Jacobi iterations and the correction by aggragation of unknowns. Our considerations are restricted to a simple one-dimensional example, which allows us to employ the technique of the Fourier analysis. Despite of this restriction we are able to demonstrate differences between the behaviour of the algorithm considered and of multigrid methods employing interpolation instead of aggregation.

A multilevel preconditioner for the mortar method for nonconforming P1 finite element

Talal Rahman, Xuejun Xu (2009)

ESAIM: Mathematical Modelling and Numerical Analysis

A multilevel preconditioner based on the abstract framework of the auxiliary space method, is developed for the mortar method for the nonconforming P1 finite element or the lowest order Crouzeix-Raviart finite element on nonmatching grids. It is shown that the proposed preconditioner is quasi-optimal in the sense that the condition number of the preconditioned system is independent of the mesh size, and depends only quadratically on the number of refinement levels. Some numerical results confirming...

A necessary and sufficient criterion to guarantee feasibility of the interval Gaussian algorithm for a class of matrices

Günter Mayer, Lars Pieper (1993)

Applications of Mathematics

A necessary and sufficient to guarantee feasibility of the interval Gaussian algorithms for a class of matrices. We apply the interval Gaussian algorithm to an n × n interval matrix [ A ] the comparison matrix [ A ] of which is irreducible and diagonally dominant. We derive a new necessary and sufficient criterion for the feasibility of this method extending a recently given sufficient criterion.

A new block triangular preconditioner for three-by-three block saddle-point problem

Jun Li, Xiangtuan Xiong (2024)

Applications of Mathematics

In this paper, to solve the three-by-three block saddle-point problem, a new block triangular (NBT) preconditioner is established, which can effectively avoid the solving difficulty that the coefficient matrices of linear subsystems are Schur complement matrices when the block preconditioner is applied to the Krylov subspace method. Theoretical analysis shows that the iteration method produced by the NBT preconditioner is unconditionally convergent. Besides, some spectral properties are also discussed....

A new inclusion interval for the real eigenvalues of real matrices

Yinghua Wang, Xinnian Song, Lei Gao (2023)

Czechoslovak Mathematical Journal

By properties of Cvetković-Kostić-Varga-type (or, for short, CKV-type) B-matrices, a new class of nonsingular matrices called CKV-type B ¯ -matrices is given, and a new inclusion interval of the real eigenvalues of real matrices is presented. It is shown that the new inclusion interval is sharper than those provided by J. M. Peña (2003), and by H. B. Li et al. (2007). We also propose a direct algorithm for computing the new inclusion interval. Numerical examples are included to illustrate the effectiveness...

A new optimized iterative method for solving M -matrix linear systems

Alireza Fakharzadeh Jahromi, Nafiseh Nasseri Shams (2022)

Applications of Mathematics

In this paper, we present a new iterative method for solving a linear system, whose coefficient matrix is an M -matrix. This method includes four parameters that are obtained by the accelerated overrelaxation (AOR) splitting and using the Taylor approximation. First, under some standard assumptions, we establish the convergence properties of the new method. Then, by minimizing the Frobenius norm of the iteration matrix, we find the optimal parameters. Meanwhile, numerical results on test examples...

A note on certain ergodicity coeflcients

Francesco Tudisco (2015)

Special Matrices

We investigate two ergodicity coefficients ɸ ∥∥ and τn−1, originally introduced to bound the subdominant eigenvalues of nonnegative matrices. The former has been generalized to complex matrices in recent years and several properties for such generalized version have been shown so far.We provide a further result concerning the limit of its powers. Then we propose a generalization of the second coefficient τ n−1 and we show that, under mild conditions, it can be used to recast the eigenvector problem...

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